Feedback algorithms for intelligent reflecting surfaces: Phase shift matrix and single-bit feedback

This paper introduces two innovative feedback algorithms-phase shift matrix (PSM)-based and single-bit feedback (SBF)-based-that improve the efficiency of phase adjustments in intelligent reflecting surfaces (IRS). In the PSM-based algorithm, the IRS phase shift vector is selected from a predefined PSM to maximize the output signal-to-noise ratio (SNR) at the receiver. The receiver then sends back only the index of the optimal phase shift vector to the transmitter. In contrast, the SBF algorithm adjusts the IRS elements using single-bit feedback. Here, the transmitter makes a minor random alteration in the phase of each IRS element at each iteration; simultaneously, the receiver transmits an SBF, indicating whether the SNR improved or deteriorated after the current iteration. The transmitter keeps the "good" phase adjustment and throws away the "bad" ones. Simulation results are produced to compare the performance of both algorithms in terms of average bit error rate, and results show that SBF-based phase adjustment of IRS elements is better than PSM-based phase adjustment.